Kalman filtering with intermittent observations

Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.

[1]  N E Manos,et al.  Stochastic Models , 1960, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[2]  Nasser E. Nahi,et al.  Optimal recursive estimation with uncertain observation , 1969, IEEE Trans. Inf. Theory.

[3]  M. Athans,et al.  The uncertainty threshold principle: Fundamental limitations of optimal decision making under dynamic uncertainty , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[4]  M. Athans,et al.  Further results on the uncertainty threshold principle , 1977 .

[5]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[6]  Mohamed T. Hadidi,et al.  Linear recursive state estimators under uncertain observations , 1978 .

[7]  Y. Bar-Shalom,et al.  Detection thresholds for tracking in clutter--A connection between estimation and signal processing , 1985 .

[8]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[9]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[10]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

[11]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[12]  John Lygeros,et al.  Verified hybrid controllers for automated vehicles , 1998, IEEE Trans. Autom. Control..

[13]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[14]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[15]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[16]  Michael I. Jordan.  Graphical Models , 1998 .

[17]  M. Micheli.  Random Sampling of a Continuous-time Stochastic Dynamical System: Analysis, State Estimation, and Applications , 2001 .

[18]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[19]  Oswaldo Luiz V. Costa,et al.  Stationary filter for linear minimum mean square error estimator of discrete-time Markovian jump systems , 2002, IEEE Trans. Autom. Control..

[20]  Christoforos N. Hadjicostis,et al.  Feedback control utilizing packet dropping network links , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[21]  Qiang Ling,et al.  Soft real-time scheduling of networked control systems with dropouts governed by a Markov chain , 2003, Proceedings of the 2003 American Control Conference, 2003..

[22]  Andrey V. Savkin,et al.  The problem of state estimation via asynchronous communication channels with irregular transmission times , 2003, IEEE Trans. Autom. Control..

[23]  Bruno Sinopoli,et al.  Distributed control applications within sensor networks , 2003, Proc. IEEE.

[24]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[25]  Peter Seiler,et al.  Estimation with lossy measurements: jump estimators for jump systems , 2003, IEEE Trans. Autom. Control..